Modular and Efficient Divide-and-Conquer SAT Solver on Top of the Painless Framework

Abstract

Over the last decade, parallel SATisfiability solving has been widely studied from both theoretical and practical aspects. There are two main approaches. First, divide-and-conquer (D&C) splits the search space, each solver being in charge of a particular subspace. The second one, portfolio launches multiple solvers in parallel, and the first to find a solution ends the computation. However although D&C based approaches seem to be the natural way to work in parallel, portfolio ones experimentally provide better performances. An explanation resides on the difficulties to use the native formulation of the SAT problem (i.e., the CNF form) to compute an a priori good search space partitioning (i.e., all parallel solvers process their subspaces in comparable computational time). To avoid this, dynamic load balancing of the search subspaces is implemented. Unfortunately, this is difficult to compare load balancing strategies since state-of-the-art SAT solvers appropriately dealing with these aspects are hardly adaptable to various strategies than the ones they have been designed for. This paper aims at providing a way to overcome this problem by proposing an implementation and evaluation of different types of divideand-conquer inspired from the literature. These are relying on the Painless framework, which provides concurrent facilities to elaborate such parallel SAT solvers. Comparison of the various strategies are then discussed.

Centrality Heuristics for Exact Model Counting

“…We show that using centrality values computed only once at the beginning of the model counting search can already be beneficial, whereas [30] recompute betweenness centrality values at each step of a topdown compilation process. Finally, we note that our empirical observation that VSIDS is not an impactful heuristic in the context of search-based model counting agrees with recent observations on the limited applicability of VSIDS as a way to decompose search into subspaces in the context of parallel SAT solving [34].…”

Constructing 5-chromatic unit distance graphs embedded in the Euclidean plane and two-dimensional spheres

“…When checking the existence of coloring of the constructed graphs in 4 colors, SAT solvers Minisat [11], Glucose 4 and the multithreaded version Glucose-syrup [3], Maple-LCMDistChronoBT-DLv3 (MapleLCMDv3) [19], plingeling [5], painless-mcomsps [23], and Kissat [6] were used. All employed SAT solvers are based on the Conflict-Driven Clause Learning algorithm (CDCL [25]).…”

ParaQooba: A Fast and Flexible Framework for Parallel and Distributed QBF Solving

“…To the best of our knowledge, besides these two approaches no other parallel QBF solver has recently been presented. The situation in SAT is different: several very powerful parallel and distributed SAT solvers like Mallob [24], Painless [5], and the afore mentioned solver ParaCooba [7] have been released. They show the potential of parallel and distributed approaches impressively by solving hard SAT instances, for example from multiplier verification [15].…”